岡山大学環境理工学部Acta Medica Okayama1341-90991012005A permanence theorem for a mathematical model for dynamics of pathogens and cells in vivo using elementary methods911ENTsuyoshiKajiwaraToruSasakiAn elementary proof of permanence for a simple mathematical model proposed by Nowak and Bangham. In many papers, permanence property is proved by theorems established by the general theory of dynamical system. In this paper, we present an elementary proof only using differential inequalities and the theory of linear differential equations with constant coefficients.No potential conflict of interest relevant to this article was reported.岡山大学環境理工学部Acta Medica Okayama1341-90991012005力学系のパーシステンスについて（レビュー）1321ENToruSasakiTsuyoshiKajiwaraSome important results on persistence are reviewed. These results concern the behavior of the orbits approaching the boundary. The orbits restrict the flow on the boundary, if one of them approaches more than one invariant set. A typical example is a model for cyclic competition, where the heteroclinic cycle can be the ω-limit set. Thus the persistence can be reduced to some conditions on the boundary flow.No potential conflict of interest relevant to this article was reported.岡山大学環境理工学部Acta Medica Okayama1341-9099712002感染症数理モデルの安定性解析1721ENAkikoMuraseToruSasakiTsuyoshiKajiwaraDynamics of infectious disease in vivo is described by coupled differential equations. Stability analysis of the complicated systems is difficult without computer calculation, while stability analysis is, in general, important to investigate qualitative behaviour of models. Liu analyzes stability of systems describing HIV dynamics in vivo with a symbolic calculation software. The same method is used for stability analysis of a mathematical model of malaria.No potential conflict of interest relevant to this article was reported.岡山大学環境理工学部Acta Medica Okayama1341-9099612001ランダムビットストリングと抗原多様性 ―コンピュータ・シミュレーション3539ENToruSasakiTransition of random bit strings is simulated by using pseudorandom numbers. Bit strings are considered as RNA of HIV virus here. Transition of random bit strings represents that of antigenic deversity.No potential conflict of interest relevant to this article was reported.岡山大学環境理工学部Acta Medica Okayama1341-9099512000ウイルス性肝炎発病の数理モデル711ENToruSasakiTsuyoshiKajiwaraSimple mathematical models are considered to explain the pathogenesis of viral hepatitis. Dynamics of populations of liver cells and two virus strains are analyzed qualitatively. This analysis suggests the possibility that the viral mutation causes the hepatitis from the state of carrier.No potential conflict of interest relevant to this article was reported.岡山大学環境理工学部Acta Medica Okayama1341-9099512000粘弾性モデルを用いた着地衝撃シミュレーション1321ENMasahitoKokuboToruSasakiThe purpose of this study is to make some body models with viscoelastic model, to simulate the heel impact and to obtain the ground reaction force. In this paper, we build up body models of linear viscoelastic elements and mass elements to simulate heel impact. Here we consider the systems of linear differential equations numerically for the preparation of mathematical analysis in future. The simplest model with two mass elements is hardly able to simulate the heel impact if the rate of mass of elements is realistic. The models with more elements are suitable to simulate for actual rate of weight of body segments. The model with three mass elements makes it possible to guess the force to each body segment.No potential conflict of interest relevant to this article was reported.岡山大学環境理工学部Acta Medica Okayama1341-9099512000微分方程式モデルによるウイルス感染症の数理的解析：レビュー2330ENToruSasakiTsuyoshiKajiwaraSome mathematical models describing interaction of virus and cells in vivo are reviewed. Similar models using systems of ordinary differential equations can be used for the analysis of dynamics of virus and cells for different kinds of virus. Models for human immunodeficiency virus, hepatitis C virus and hepatitis B virus are treated here. Although models are similar, different approximations can reduce the systems to the explicitly solvable forms. The solutions obtained here can be used to estimate biological parameters.No potential conflict of interest relevant to this article was reported.岡山大学環境理工学部Acta Medica Okayama1341-9099311998Computational analysis of contamination in Kojima Lake using upwind-type finite element method3136ENToruSasakiTsuyoshiKajiwaraHirofumiIshikawaWe have computed the phase of spreading contaminations in Kojima Lake by using the upwind-type finite element method. We have treated the two cases: the pollutant flows from the Sasagase river and from the Kurashiki River. We see that the upwind-type finite element method is effective in both cases, when the diffusion constant is quite small.No potential conflict of interest relevant to this article was reported.岡山大学環境理工学部Acta Medica Okayama1341-9099111996Computational water analysis in an artificial lake: Kojima Lake case4753ENToruSasakiHirofumiIshikawaTsuyoshiKajiwaraMasajiWatanabeWe treat the problem of water pollution by the method of a mathematical model. We illustrate the method of analysis with Kojima Lake. We analyze in-flow and out-flow of the lake, compute numerical solutions of the governing equations of the water flow and the pollutant. The simulation leads to the conclusion concerning the figure of Kojima Lake.No potential conflict of interest relevant to this article was reported.